Model parameters (condensed).

Free parameters are listed for the 72 behavioral models in ascending order of complexity within and across classes. The models are coded with the first letter of the label referring to four possibilities: an absence of learning (“X”), reinforcement learning (RL) without generalization (“0”), generalized reinforcement learning (GRL) with one shared generalization parameter g1 (“1”), or GRL with two separate generalization parameters g1 and g2 (“2”). RL itself required free parameters for the learning rate α and the softmax temperature τ. Models labeled with “C” for the second letter included a constant lateral bias, which was arbitrarily designated as a rightward bias βR (where βR < 0 is leftward). The list is condensed with bracket notation to represent the range for the n-back horizons of each successive model within a hysteresis category (e.g., “2CE[1–3]” for models 2CE1, 2CE2, and 2CE3). Models labeled with”N” and ending with a positive integer (from the range in brackets) included n-back hysteresis with free parameters βn for repetition (βn > 0) or alternation (βn < 0) of each previous action represented—up to 4 trials back (β4) with learning and up to 8 trials back (β8) without learning. Models labeled with “E” and ending with a positive integer N (from the range in brackets) included exponential hysteresis with inverse decay rate λH taking effect N+1 trials back. Exponential models could also be both parametric and nonparametric with N free parameters βn for initial n-back hysteresis up to 3 trials back (β3), where the final βN is the initial magnitude of the exponential component. “df” stands for degrees of freedom. See also Table A in S1 Text for the unrolled version of the list. This ordering of the models corresponds to the ordering in Figs 2 and 3.